Scaliing in Three-Dimensional Foams

Abstract

AbstractThe coarsening and internal dynamics of a bulk foam are probed noninvasively by exploiting the strong multiple scattering of light that gives foams their familiar white color. By approximating the light propagation as a diffusion process, transmission measurements provide a direct probe of the average bubble size d. A second corroborating measure of d is obtained by analyzing temporal intensity fluctuations of the multiply scattered light within the framework of diffusing-wave spectroscopy. Both sets of measurements show the same behavior: At early times d is approximately a constant (20µm). After about twenty minutes the foam begins to coarsen and scaling behavior is observed such that the growth of d is a power-law in time, tz with z=0.45±0.05. This result is in near accord with the theoretical prediction, z=1/2, for foam in the limiting case of space-filling polyhedral bubbles. In addition, the change in packing conditions during coarsening gives rise to a nonequilibrium dynamical process which also exhibits temporal scaling: Neighboring bubbles undergo sudden structural rearrangements at a rate per unit volume which decays as t−Y with y=2.0±0.2. This value of y cannot be explained by the presence of only a single time-dependent length scale in the foam structure. Since these bubble rearrangement events serve to relax local stress, they must also play a role in the relaxation of externally imposed stress. Therefore, elucidation of their origin and scaling behavior will lead to an increased understanding of the rheology and stability of foams.